Food Price Transmisson
Price transmission effects through
three stages of food production
An analysis of price transmission through three stages of food
production reveals substantial differences in price transmission
from producer food to consumer food consumed at home
versus that consumed away from home; increases in various
food-related PPIs lead to increases in the CPI for food consumed
at home but not the CPI for food consumed away from home
Jonathan C. Weinhagen
Jonathan C. Weinhagen
is an economist in the
Division of Producer
Price Indexes, Bureau of
Labor Statistics. Email:
weinhagen.jonathan@
bls.gov.
A
ccording to the Consumer Expenditure Survey (CE) of the Bureau
of Labor Statistics, U.S. consumers
spent $6,129, on average, on food in 2010,
accounting for close to 13 percent of average household annual expenditures. Of total
household food expenditures, approximately
60 percent ($3,624) was spent on food consumed at home and 40 percent ($2,505) was
spent on food consumed away from home.
The CE defines food consumed at home as
food purchased from grocery stores or other
food stores. The CE defines food consumed
away from home as meals (including takeout) purchased from restaurants, vending
machines, and mobile vendors.
Given the relatively large share of
household spending made up by food,
changes in food prices can affect consumer
welfare substantially. Over the past decade,
prices for unprocessed foods have risen
considerably. From December 2001 to
May 2011, the Producer Price Index (PPI)
for unprocessed foodstuffs and feedstuffs
(also known as the PPI for crude foodstuffs
and feedstuffs) increased approximately
90 percent. This article uses econometric
techniques to examine price transmission
through three stages of food production:
unprocessed producer foods, finished
producer food that eventually will be sold
to consumers, and consumer food. The
article analyzes price transmission effects
on consumer food, not only overall, but also
separately for that expenditure category’s two
components: food consumed at home and
food consumed away from home. Analysts
expect that price transmission from producer
food to food consumed at home differs from
price transmission from producer food to
food consumed away from home, because
the service of preparing food may represent
a substantial component of the value of food
consumed away from home.
The article begins by using a vector
autoregression (VAR) model to analyze price
transmission from producer food to total
consumer food. Then, in the next section,
two separate VAR models are used to examine
whether there are differences in price
transmission from producer food to consumer
food purchased for home consumption as
opposed to consumer food consumed away
from home. Finally, conclusions drawn from
the analysis are presented.
Producer food to total CPI food
VAR models can be used to examine the causal
relationships between food prices at three
stages of food production. VAR modeling
involves estimating a series of equations in
Monthly Labor Review • December 2012 19
Food Price Transmission
which each variable is expressed as a linear combination
of itself and all other variables in the system.1 A threevariable VAR model (henceforth referred to as VAR-TOTAL
because it includes total food) using the PPI for unprocessed
foodstuffs and feedstuffs, the PPI for finished consumer
food, and the Consumer Price Index (CPI) for total food
was estimated with monthly data from January 1980
through May 2011. The PPI for unprocessed foodstuffs and
feedstuffs measures price changes in unprocessed foods and
feeds sold to businesses as inputs to production. The PPI for
finished consumer food measures price changes received
by manufacturers of both processed and unprocessed food
that will eventually be sold to consumers. The CPI for total
food measures the average change in the selling price that
consumers pay for food and includes both food consumed
at home and food consumed away from home.
All data used in this article were seasonally adjusted and
converted to percentage-growth form by taking the first
differences of their natural logarithms. Converting timeseries data to percentage-growth form typically induces
stationarity in the data. A time series is stationary if
the mean, variance, and covariance of the series are not
dependent on time. Using nonstationary time series to
estimate a VAR model invalidates conventional significance
tests of the model’s coefficients and can treat insignificant
correlations as significant, even if both variables follow
mostly independent trends. Dickey–Fuller tests were used
to determine whether the series, expressed in percentagegrowth terms, were stationary.2 The tests included trends,
intercepts, and sufficient lags to ensure white-noise
residuals. The tests indicated that all of the time series used
were stationary when expressed in percentage-growth
terms. To determine the correct lag structure of the VAR,
the Schwarz information criterion was implemented.3
The criterion suggested that a VAR whose equations have
one lag is optimal; therefore, one lag of each variable was
used to estimate the VAR.
The VAR model was first used to test for Granger causality
among the indexes. A variable is said to Granger-cause a
second variable when adding past values of the variable to
an autoregressive model of the second variable improves
the predictability of the latter. Wald statistics were used
to test the null hypothesis that there was no Granger
causality. Wald tests are based on measuring the extent
to which the unrestricted estimates fail to satisfy the
restrictions of the null hypothesis.4 A small p-value of the
Wald statistic rejects the null hypothesis that there is no
feedback to the dependent variable, and a large p-value of
the Wald statistic implies that the null hypothesis is not
rejected. A p-value of less than 0.01 indicates rejection
of the null hypothesis at the 99-percent confidence level,
whereas a p-value of 0.05 or less indicates rejection of
the null hypothesis at the 95-percent confidence level. A
p-value greater than 0.05 suggests acceptance of the null
hypothesis that there is no Granger causality.
In addition to testing for Granger causality from
individual indexes to the dependent variable, the analysis
tested the joint lagged values of variables at stages of
processing before and after the dependent variable for
Granger causality. For example, the null hypothesis that
prices for unprocessed foods and feeds and for finished
consumer food do not jointly Granger-cause the CPI for
total food was tested. Table 1 presents the results of the
Granger causality tests.
The tests indicate that food prices at earlier stages of
production generally Granger-cause food prices at more
processed stages of production but that food prices at later
stages of production do not Granger-cause food prices
Table 1. Results of the Granger causality tests
VAR-TOTAL: Null hypothesis
Dependent variable: PPI for unprocessed foodstuffs and feedstuffs
Chi-square
p-value
PPI for finished consumer food = 0
0.070
0.791
CPI for total food = 0
2.083
.149
PPI for finished consumer foods/CPI for total food = 0
2.911
.233
25.109
.000
1.012
.315
Dependent variable: PPI for finished consumer food
PPI for unprocessed foodstuffs and feedstuffs = 0
CPI for total food = 0
Dependent variable: CPI for total food
.354
.552
PPI for finished consumer food = 0
23.308
.000
PPI for unprocessed foodstuffs and feedstuffs/PPI for finished consumer food = 0
46.092
.000
PPI for unprocessed foodstuffs and feedstuffs = 0
20 Monthly Labor Review • December 2012
at earlier stages of production. The tests show that the PPI
for unprocessed foodstuffs and feedstuffs Granger-causes
the PPI for finished consumer food, the PPI for finished
consumer food Granger-causes the CPI for total food, and
the PPI for unprocessed foodstuffs and feedstuffs and the PPI
for finished consumer food jointly Granger-cause the CPI
for total food. By contrast, the CPI for total food does not
Granger-cause the PPI for finished consumer food, the CPI
for total food does not Granger-cause the PPI for unprocessed
foodstuffs and feedstuffs, the PPI for finished consumer food
does not Granger-cause the PPI for unprocessed foodstuffs
and feedstuffs, and the CPI for total food and the PPI for
finished consumer food do not jointly Granger-cause the PPI
for unprocessed foodstuffs and feedstuffs.
VAR coefficients are difficult to interpret because of the
multivariate nature of the models. Accordingly, impulse
response functions and variance decompositions were
developed to assist in interpreting VARs. Impulse response
functions measure the effect of a one-standard-deviation
perturbation of a variable in a system of equations on
current and future values of all variables in the system.
Variance decompositions show the percentage of forecast
error variance in one variable of the VAR that is explained
by perturbations to all variables used in the VAR.5 Because
shocks within a VAR are generally not contemporaneously
independent of each other, a random shock to one
variable often occurs simultaneously with shocks to
other variables. To overcome this problem, the residuals
may be orthogonalized by a Cholesky decomposition
in which the covariance matrix of the residuals is lower
triangular. Therefore, a shock to one variable in the system
contemporaneously affects only variables ordered after
that variable in the VAR.6
The residuals of the VAR were orthogonalized by a
Cholesky decomposition using the following ordering:
PPI for unprocessed foodstuffs and feedstuffs, PPI for
finished consumer food, and CPI for total food. This
ordering was chosen because unprocessed foods and feeds
are used as inputs to produce finished consumer foods,
which are then used as inputs to CPI food. In addition,
the Wald tests that were carried out indicated that the PPI
for unprocessed foodstuffs and feedstuffs Granger-causes
the PPI for finished consumer food and that the PPI for
finished consumer food Granger-causes the CPI for food.
Subsequent to orthogonalization of the residuals, impulse
response functions and variance decompositions were
constructed from the VAR coefficients.
Chart 1 presents the accumulated impulse response
functions of one-standard-deviation shocks to the three
variables in the system. Standard error bands (dashed
red lines) were constructed with the use of the software
program EVIEWS 5.0 to represent the statistical significance
of the impulse response functions. The impulse responses
were found to be significant at the 95-percent confidence
level when both standard error bands were simultaneously
above or below zero on the y-axis.
The impulse response functions show that changes in
prices are passed forward through the three stages of food
production. In all cases, price shocks at earlier stages of
food production lead to statistically significant changes in
prices at later stages of food production. For example, a onestandard-deviation (2.4-percent) unanticipated increase in
the PPI for unprocessed foodstuffs and feedstuffs leads to a
0.7-percent increase in the PPI for finished consumer food.
More than half of the impact of the unprocessed-food
shock on the PPI for finished consumer food occurs in the
same month as the shock, and the full impact is reached
after 4 months. A one-standard-deviation (2.4-percent)
unanticipated increase in the PPI for unprocessed foodstuffs
and feedstuffs leads to a 0.17-percent increase in the CPI
for total food. Approximately a quarter of the impact of
the unprocessed-food shock occurs in the same month as
the shock, and the full impact is reached after 6 months.
Likewise, a one-standard-deviation (0.58-percent) increase in the PPI for finished consumer food results in a
0.21-percent rise in the CPI for total food. By contrast,
the impulse response functions do not suggest that price
changes are passed backward through the stages of food
production: in no instances does an unanticipated change
to an index at a later stage of food production lead to a
statistically significant change to an index at an earlier
stage of food production.
Table 2 presents the variance decompositions for the
stage-of-processing food indexes after 12 months. Like the
impulse response functions, the variance decompositions
imply that price shocks are passed forward, and not
backward, through the stages of food production.
Table 2 shows that 11.35 percent of the forecast error
variance in the CPI for total food can be attributed to
shocks to the PPI for unprocessed foodstuffs and feedstuffs
while 23.93 percent is attributable to finished consumer
food. Alternatively, less than 0.5 percent of the forecast
error variance in the PPIs for unprocessed foodstuffs and
feedstuffs and for finished consumer food can be explained
by shocks to CPI food.
In sum, the Granger causality tests, impulse response
functions, and variance decompositions all indicate that
changes in producer prices for unprocessed foods and
feeds, as well as changes in producer prices for finished
consumer food, are transmitted forward to prices for
Monthly Labor Review • December 2012 21
Food Price Transmission
Chart 1. Accumulated impulse response functions from VAR-TOTAL
Shock to—
Response
PPI for unprocessed foodstuffs and feedstuffs
of—
0.04
0.04
PPI for
.03
.03
.02
.02
.02
.01
.01
.00
.00
.00
–.01
1
2
3
4
5
6
7
8
9 10 11 12
total
food
–.01
1
2
3
4
5
6
7
8
–.01
1
9 10 11 12
0.010
0.010
0.010
.008
.008
.008
.006
.006
.006
.004
.004
.002
.002
finished
.004
consumer
food
.002
CPI for
0.04
.03
unprocessed
foodstuffs
.01
and
feedstuffs
PPI for
CPI for total food
PPI for finished consumer food
.000
.000
.000
–.002
–.002
–.002
1
2
3
4
5
6
7
8
9 10 11 12
1
2
3
4
5
6
7
8
9 10 11 12
1
0.0035
0.0035
0.0035
.0030
.0030
.0030
.0025
.0025
.0025
.0020
.0020
.0020
.0015
.0015
.0015
.0010
.0010
.0010
.0005
.0005
.0005
.0000
1
2
3
4
5
6
7
8
.0000
9 10 11 12
1
2
3
4
5
6
7
8
9 10 11 12
.0000
1
2
3
4
5
6
7
8
9 10 11 12
2
3
4
5
6
7
8
9 10 11 12
2
3
4
5
6
7
8
9 10 11 12
Table 2. Variance decompositions from VAR-TOTAL after 12 months
Percentage of forecast error due to—
Decomposition variable
PPI for unprocessed
foodstuffs and feedstuffs
PPI for finished consumer
CPI for total food
food
PPI for unprocessed foodstuffs and feedstuffs
99.18
0.32
0.49
PPI for finished consumer food
43.30
56.47
.23
CPI for total food
11.35
23.93
64.72
consumer food. The tests also suggest that price changes
for foods are not passed backward through the stages of
food production.
Producer food to CPI food consumed at home
and away from home
This section uses two separate VAR models to examine
22 Monthly Labor Review • December 2012
whether there are differences in price transmission from
producer food to consumer food purchased for home
consumption versus consumer food consumed away from
home. The first VAR, composed of the PPI for unprocessed
foodstuffs and feedstuffs, the PPI for finished consumer
food, and the CPI for food consumed at home, will be
referred to as VAR-HOME. The second VAR, composed of
the PPI for unprocessed foodstuffs and feedstuffs, the PPI
for finished consumer food, and the CPI for food consumed
away from home, will be referred to as VAR-AWAY.7
Estimating two separate VARs—one that includes the CPI
for food consumed at home as the final stage and the other
that instead includes the CPI for food consumed away from
home as the final stage—allows for a separate examination
of price transmission effects on food consumed at home
versus food consumed away from home. As mentioned
earlier, it might be expected that the price transmission
effects from producer food to consumer food consumed
away from home would be less than those to consumer
food consumed at home, because the former includes the
service of food preparation as a substantial component.
One lag of monthly seasonally adjusted data from
January 1980 through May 2011 was used to estimate the
two VARs. All data were seasonally adjusted and converted
to percentage-growth form by taking first differences of
their natural logarithms. Dickey–Fuller tests that were
run indicated that all series expressed in percentagegrowth form were stationary. The VAR models were used
to examine Granger causality among prices at the three
stages of production. Table 3 displays the results of the
Granger causality tests.
The results of the Granger causality tests developed
from VAR-HOME and VAR-AWAY are similar to each
other and to those from VAR-TOTAL, which includes total
foods. For both VAR-HOME and VAR-AWAY, Granger
causality occurs only from indexes at earlier stages of food
production to those at later stages of food production.
The Granger causality tests, therefore, do not provide
strong evidence of differences in price pass-through from
producer food prices to consumer food prices for food
Table 3. Results of the Granger causality tests
Variables
Chi-square
p-value
VAR-HOME: Null hypothesis
Dependent variable: PPI for unprocessed foodstuffs and feedstuffs
Independent variable:
PPI for finished consumer food = 0
0.109
0.742
CPI for food at home = 0
1.525
.217
PPI for finished consumer food/CPI for food at home = 0
2.351
.309
Dependent variable: PPI for finished consumer food
Independent variable:
PPI for unprocessed foodstuffs and feedstuffs = 0
CPI for food at home = 0
Dependent variable: CPI for food at home
Independent variable:
24.588
.000
.388
.534
PPI for unprocessed foodstuffs and feedstuffs = 0
.962
.327
PPI for finished consumer food = 0
28.884
.000
PPI for unprocessed foodstuffs and feedstuffs/PPI for finished consumer food = 0
60.369
.000
VAR-AWAY: Null hypothesis
Dependent variable: PPI for unprocessed foodstuffs and feedstuffs
Independent variable:
PPI for finished consumer food = 0
.542
.462
CPI for food away from home = 0
2.120
.145
PPI for finished consumer food/CPI for food away from home = 0
2.948
.229
Dependent variable: PPI for finished consumer food
Independent variable:
PPI for unprocessed foodstuffs and feedstuffs = 0
CPI for food away from home = 0
Dependent variable: CPI for food away from home
Independent variable:
PPI for unprocessed foodstuffs and feedstuffs = 0
26.121
.000
2.515
.113
.518
.472
PPI for finished consumer food = 0
6.434
.011
PPI for unprocessed foodstuffs and feedstuffs/PPI for finished consumer food = 0
7.963
.019
Monthly Labor Review • December 2012 23
Food Price Transmission
consumed at home versus food consumed away from
home.
In addition to playing their role in Granger causality tests,
the two VARs estimated in this section were used to develop
impulse response functions and variance decompositions.
As with VAR-TOTAL in the previous section, the residuals
were orthogonalized by a Cholesky decomposition with
the following ordering: PPI for unprocessed foodstuffs
and feedstuffs, PPI for finished consumer food, and CPI
for food consumed at home (for VAR-HOME) or CPI for
food consumed away from home (for VAR-AWAY). Chart
2 presents the accumulated impulse response functions
developed from the coefficients of VAR-HOME, while
chart 3 shows the response functions developed from the
coefficients of VAR-AWAY.
In contrast to the Granger causality tests presented
in table 3, the impulse response functions suggest that
there are substantial differences in how price changes
are transmitted from producer food to consumer food
consumed at home versus consumer food consumed
away from home. A comparison of the impulse response
functions in charts 2 and 3 shows that unanticipated
price changes in the PPI for unprocessed foodstuffs and
feedstuffs significantly affect the CPI for food consumed
at home but do not significantly affect the CPI for food
consumed away from home. In addition, the impulse
response functions indicate that unanticipated changes to
the PPI for finished consumer food significantly affect both
the CPI for food consumed at home and the CPI for food
consumed away from home but that the effect is much
Chart 2. Accumulated impulse response functions from VAR-HOME
Shock to—
PPI for unprocessed foodstuffs and feedstuffs
PPI for finished consumer food
CPI for food consumed at home
Response 0.04
of—
0.04
0.04
.03
.03
.03
unprocessed .02
foodstuffs
.01
and
feedstuffs
.02
.02
.01
.01
.00
.00
PPI for
.00
–.01
1
PPI for
2
3
4
5
6
7
8
9 10 11 12
1
2
3
4
5
6
7
8
9 10 11 12
–.01
0.010
0.010
0.010
.008
.008
.008
.006
.006
.006
.004
.004
.002
.002
.002
.000
.000
finished
consumer .004
food
–.002
CPI for
–.01
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
9 10 11 12
1
2
3
4
5
6
7
8
9 10 11 12
4
5
6
7
8
9 10 11 12
.000
–.002
1
9 10 11 12
2
3
4
5
6
7
8
9 10 11 12
–.002
0.005
0.005
0.005
.004
.004
.004
.003
.003
.003
.002
.002
.001
.001
food
consumed .002
at home
.001
.000
1
2
3
4
5
6
7
8
24 Monthly Labor Review • December 2012
9 10 11 12
.000
1
2
3
4
5
6
7
8
9 10 11 12
.000
1
2
3
Chart 3. Accumulated impulse response functions from VAR-AWAY
Shock to—
Response PPI for unprocessed foodstuffs and feedstuffs
of—
0.04
0.04
PPI for finished consumer food
CPI for food consumed away from home
0.04
.03
.03
.03
unproc- .02
essed
.01
foodstuffs and .00
feedstuffs
.02
.02
.01
.01
.00
.00
–.01
–.01
PPI for
–.01
–.02
PPI for
1
2
3
4
5
6
7
8
9 10 11 12
2
3
4
5
6
7
8
9 10 11 12
–.02
1
0.010
0.010
.008
.008
.008
.006
.006
.006
.004
.004
.002
.002
.002
.000
.000
.000
–.002
food
consumed
away
from
home
1
0.010
finished
consum- .004
er food
CPI for
–.02
1
2
3
4
5
6
7
8
9 10 11 12
–.002
1
2
3
4
5
6
7
8
9 10 11 12
–.002
2
3
4
5
6
7
8
9 10 11 12
1
2
3
4
5
6
7
8
9 10 11 12
2
7
8
9 10 11 12
0.005
0.005
0.005
.004
.004
.004
.003
.003
.003
.002
.002
.002
.001
.001
.001
.000
.000
.000
–.001
1
–.001
1
–.001
1
2
3
4
5
6
7
8
9 10 11 12
2
3
4
stronger for food consumed at home. A one-standarddeviation (0.58-percent) shock to the PPI for finished
consumer food leads to a 0.29-percent increase in the CPI
for food consumed at home, but to only a 0.05-percent
increase in the CPI for food consumed away from home.
Furthermore, the shock to finished consumer food has an
immediate effect on the CPI for food consumed at home,
and the full impact of the shock occurs after 4 months.
The shock to finished consumer food, by contrast, does
not initially affect the CPI for food consumed away from
home, and the full effects of the shock are not realized for 8
months. The impulse response function analysis, therefore,
supports the hypothesis that changes to producer food
prices are transmitted more strongly to consumer prices
for food consumed at home than to consumer prices for
5
6
7
8
9 10 11 12
3
4
5
6
food consumed away from home.
Table 4 presents the variance decompositions of VARHOME and VAR-AWAY. Like the impulse response
functions, the variance decompositions suggest that the
price transmission effects from producer food to consumer
food are much stronger for food consumed at home than
for food consumed away from home.
The variance decompositions in table 4 show that 13.33
percent of the forecast error variance in the CPI for food
consumed at home can be attributed to unanticipated
changes to the PPI for unprocessed foodstuffs and feedstuffs
while 24.65 percent is attributable to the PPI for finished
consumer food. Alternatively, the variance decompositions
indicate that only 0.46 percent of the forecast error
variance in the CPI for food consumed away from home
Monthly Labor Review • December 2012 25
Food Price Transmission
Table 4. Variance decompositions
Percentage of forecast error due to—
Decomposition variable
PPI for unprocessed
foodstuffs and feedstuffs
PPI for finished consumer
food
PPI for unprocessed foodstuffs and feedstuffs
99.36
0.30
PPI for finished consumer food
43.02
56.86
.11
CPI for food at home
13.33
24.65
62.02
PPI for unprocessed foodstuffs and feedstuffs
99.05
.17
.77
PPI for finished consumer food
43.73
55.90
.38
.46
2.11
97.43
CPI for food at home
VAR-HOME
0.34
VAR-AWAY
CPI for food away from home
can be explained by unexpected changes to the PPI for
unprocessed foodstuffs and feedstuffs while 2.11 percent
is explainable by the PPI for finished consumer food. The
vast majority (97.43 percent) of the forecast error variance
in the CPI for food consumed away from home is due to
unanticipated changes in that variable itself.
THIS ARTICLE HAS PRESENTED estimated VAR
models for studying price transmission through three stages
of food production, the final stage of which is consumer
food. The issue examined by the article was whether price
transmission from producer food to consumer food differed
for consumer food purchased for home consumption versus
food consumed away from home.
The analysis began by estimating a VAR with three
variables: the PPI for unprocessed foodstuffs and feedstuffs, the PPI for finished consumer food, and the CPI
for total food. The VAR was used to test for Granger
causality and to construct impulse response functions
and variance decompositions. The Granger causality tests,
impulse response functions, and variance decompositions
all indicated that price changes are transmitted forward
through the stages of food production, but not backward.
For example, the impulse response functions suggested
that a one-standard-deviation (2.4-percent) unanticipated
increase in the PPI for unprocessed foodstuffs and feedstuffs
leads to a statistically significant 0.7-percent increase in the
PPI for finished consumer food and a statistically significant
0.17-percent increase in the CPI for total food and that
a one-standard-deviation (0.58-percent) increase in the
PPI for finished consumer food results in a statistically
significant 0.21-percent rise in the CPI for total food. In
no instances did an unanticipated change in a stage-ofprocessing food index lead to a statistically significant
change in an index at an earlier stage of food production.
26 Monthly Labor Review • December 2012
The analysis then estimated two separate VARs: one that
included the CPI for food consumed at home as the final
stage and the other that instead included the CPI for food
consumed away from home as the final stage. Estimating
these two VARs allowed for a separate examination of price
transmission effects on food consumed at home versus
food consumed away from home. The impulse response
functions and variance decompositions constructed from
the VARs suggest that there are substantial differences
in price transmission from producer food to consumer
food consumed at home versus that consumed away from
home. Specifically, the impulse response functions indicate
that an unanticipated change to the PPI for unprocessed
foodstuffs and feedstuffs leads to a statistically significant
increase in the CPI for food consumed at home but does
not significantly affect the CPI for food consumed away
from home. In addition, a shock to the PPI for finished
consumer food significantly affects both the CPI for food
consumed at home and the CPI for food consumed away
from home, but the effect is much lower on the latter.
A one-standard-deviation (0.58-percent) shock to the
PPI for finished consumer food causes a 0.29-percent
increase in the CPI for food consumed at home but just a
0.05-percent increase in the CPI for food consumed away
from home. The variance decompositions tell a similar
story: on the one hand, 13.33 percent of the forecast
error variance in the CPI for food consumed at home
can be attributed to unanticipated changes to the PPI for
unprocessed foodstuffs and feedstuffs while 24.65 percent
is attributable to the PPI for finished consumer food; on
the other hand, only 0.46 percent of the forecast error
variance in the CPI for food consumed away from home
can be explained by unexpected changes to the PPI for
unprocessed foodstuffs and feedstuffs while 2.11 percent
is explainable by the PPI for finished consumer food.
Notes
1
William H. Greene, Econometric Analysis (Upper Saddle River, NJ,
Prentice Hall, 1997); see especially pp. 815–816.
David A. Dickey and Wayne A. Fuller, “Distribution of the
Estimators for Autoregressive Time Series with a Unit Root,” Journal
of the American Statistical Association, vol. 74, 1979, pp. 427–431. Also
in John Dinardo and Jack Johnston, Econometric Methods (New York,
McGraw Hill, 1996); see especially pp. 224–225.
2
Philip Hans Franses, Time Series Models for Business and Economic
Forecasting (Cambridge, U.K., Cambridge University Press, 1998).
3
Greene, Econometric Analysis, p. 161.
4
Dinardo and Johnston, Econometric Methods, pp. 289–301.
5
Ibid.
6
The CPI program prices food away from home bimonthly in most
CPI geographical areas. Therefore, the effects of a shock to a PPI foods
7
index on the foods-away-from-home index may have a 1-month lag
compared with the effects on the food-at-home index, which the CPI
program prices monthly everywhere.
Monthly Labor Review • December 2012 27